We predict the metallicity distribution of stars and the age-metallicity relation for 6 Dwarf Spheroidal ( dSph ) galaxies of the Local Group by means of a chemical evolution model which is able to reproduce several observed abundance ratios and the present day total mass and gas content of these galaxies .
The model adopts up to date nucleosynthesis and takes into account the role played by supernovae of different types ( II , Ia ) allowing us to follow in detail the evolution of several chemical elements ( H , D , He , C , N , O , Mg , Si , S , Ca , and Fe ) .
Each galaxy model is specified by the prescriptions of the star formation rate and by the galactic wind efficiency chosen to reproduce the main features of these galaxies .
These quantities are constrained by the star formation histories of the galaxies as inferred by the observed color-magnitude diagrams ( CMD ) .
The main conclusions are : i ) five of the six dSphs galaxies are characterized by very low star formation efficiencies ( \nu = 0.005 - 0.5 Gyr ^ { -1 } ) with only Sagittarius having a higher one ( \nu = 1.0 - 5.0 Gyr ^ { -1 } ) ; ii ) the wind rate is proportional to the star formation rate and the wind efficiency is high for all galaxies , in the range w _ { i } = 6 - 15 ; iii ) a high wind efficiency is required in order to reproduce the abundance ratios and the present day gas mass of the galaxies ; iv ) the predicted age-metallicity relation implies that the stars of the dSphs reach solar metallicities in a time-scale of the order of 2 - 6 Gyr , depending on the particular galaxy ; v ) the metallicity distributions of stars in dSphs exhibit a peak around [ Fe/H ] \sim -1.8 to -1.5 dex , with the exception of Sagittarius , which shows a peak around [ Fe/H ] \sim 
-0.8 dex ; iv ) the predicted metallicity distributions of stars suggest that the majority of stars in dSphs are formed in a range of metallicity in agreement with the one of the observed stars .